2b_equations.gms 86.5 KB
Newer Older
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
$ontext
This file is part of Backbone.

Backbone is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

Backbone is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License
along with Backbone.  If not, see <http://www.gnu.org/licenses/>.
$offtext

18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
* =============================================================================
* --- Penalty Definitions -----------------------------------------------------
* =============================================================================

$setlocal def_penalty 1e6
Scalars
    PENALTY "Default equation violation penalty" / %def_penalty% /
;
Parameters
    PENALTY_BALANCE(grid) "Penalty on violating energy balance eq. (EUR/MWh)"
    PENALTY_RES(restype, up_down) "Penalty on violating a reserve (EUR/MW)"
;
PENALTY_BALANCE(grid) = %def_penalty%;
PENALTY_RES(restype, up_down) = %def_penalty%;


* =============================================================================
* --- Equation Declarations ---------------------------------------------------
* =============================================================================

38
equations
39
    // Objective Function, Energy Balance, and Reserve demand
40
    q_obj "Objective function"
41
    q_balance(grid, node, mType, f, t) "Energy demand must be satisfied at each node"
42
    q_resDemand(restype, up_down, node, f, t) "Procurement for each reserve type is greater than demand"
43
44

    // Unit Operation
45
46
    q_maxDownward(mType, grid, node, unit, f, t) "Downward commitments will not undercut power plant minimum load constraints or maximum elec. consumption"
    q_maxUpward(mType, grid, node, unit, f, t) "Upward commitments will not exceed maximum available capacity or consumed power"
Juha Kiviluoma's avatar
Juha Kiviluoma committed
47
    q_startup(unit, f, t) "Capacity started up is greater than the difference of online cap. now and in the previous time step"
48
49
50
51
52
53
54
55
56
57
    q_startuptype(mType, starttype, unit, f, t) "Startup type depends on the time the unit has been non-operational"
    q_onlineLimit(mType, unit, f, t) "Number of online units limited for units with startup constraints and investment possibility"
    q_onlineMinUptime(mType, unit, f, t) "Unit must stay operational if it has started up during the previous minOperationTime hours"
*    q_minDown(mType, unit, f, t) "Unit must stay non-operational if it has shut down during the previous minShutDownTime hours"
*    q_genRamp(grid, node, mType, s, unit, f, t) "Record the ramps of units with ramp restricitions or costs"
*    q_genRampChange(grid, node, mType, s, unit, f, t) "Record the ramp rates of units with ramping costs"
*    q_rampUpLimit(grid, node, mType, s, unit, f, t) "Up ramping limited for units"
*    q_rampDownLimit(grid, node, mType, s, unit, f, t) "Down ramping limited for units"
    q_outputRatioFixed(grid, node, grid, node, unit, f, t) "Force fixed ratio between two energy outputs into different energy grids"
    q_outputRatioConstrained(grid, node, grid, node, unit, f, t) "Constrained ratio between two grids of energy output; e.g. electricity generation is greater than cV times unit_heat generation in extraction plants"
58
    q_conversionDirectInputOutput(effSelector, unit, f, t) "Direct conversion of inputs to outputs (no piece-wise linear part-load efficiencies)"
Juha Kiviluoma's avatar
Juha Kiviluoma committed
59
60
61
    q_conversionSOS2InputIntermediate(effSelector, unit, f, t)   "Intermediate output when using SOS2 variable based part-load piece-wise linearization"
    q_conversionSOS2Constraint(effSelector, unit, f, t)          "Sum of v_sos2 has to equal v_online"
    q_conversionSOS2IntermediateOutput(effSelector, unit, f, t)  "Output is forced equal with v_sos2 output"
62
63
64
65
66
67
68
69
70
71
72
    q_fixedGenCap1U(grid, node, unit, t) "Fixed capacity ratio of a unit in one node versus all nodes it is connected to"
    q_fixedGenCap2U(grid, node, unit, grid, node, unit, t) "Fixed capacity ratio of two (grid, node, unit) pairs"

    // Energy Transfer
    q_transfer(grid, node, node, f, t) "Rightward and leftward transfer must match the total transfer"
    q_transferRightwardLimit(grid, node, node, f, t) "Transfer of energy and capacity reservations to the rightward direction are less than the transfer capacity"
    q_transferLeftwardLimit(grid, node, node, f, t) "Transfer of energy and capacity reservations to the leftward direction are less than the transfer capacity"
    q_resTransferLimitRightward(grid, node, node, f, t) "Transfer of energy and capacity reservations are less than the transfer capacity to the rightward direction"
    q_resTransferLimitLeftward(grid, node, node, f, t) "Transfer of energy and capacity reservations are less than the transfer capacity to the leftward direction"

    // State Variables
73
    q_stateSlack(grid, node, slack, f, t) "Slack variable greater than the difference between v_state and the slack boundary"
74
75
    q_stateUpwardLimit(grid, node, mType, f, t) "Limit the commitments of a node with a state variable to the available headrooms"
    q_stateDownwardLimit(grid, node, mType, f, t) "Limit the commitments of a node with a state variable to the available headrooms"
76
*    q_boundState(grid, node, node, mType, f, t) "Node state variables bounded by other nodes"
77
    q_boundStateMaxDiff(grid, node, node, mType, f, t) "Node state variables bounded by other nodes (maximum state difference)"
78
    q_boundCyclic(grid, node, mType, s, f, t, s_, f_, t_) "Cyclic bound for the first and the last states of samples"
79
80
81
*    q_boundCyclicSamples(grid, node, mType, s, f, t, s_, f_, t_) "Cyclic bound inside or between samples"

    // Policy
82
    q_capacityMargin(grid, node, f, t) "There needs to be enough capacity to cover energy demand plus a margin"
Niina Helistö's avatar
Niina Helistö committed
83
    q_emissioncap(gngroup, emission) "Limit for emissions"
84
    q_instantaneousShareMax(gngroup, group, f, t) "Maximum instantaneous share of generation and controlled import from a group of units and links"
Niina Helistö's avatar
Niina Helistö committed
85
86
    q_energyShareMax(gngroup, group) "Maximum energy share of generation and import from a group of units"
    q_energyShareMin(gngroup, group) "Minimum energy share of generation and import from a group of units"
87
    q_inertiaMin(gngroup, f, t) "Minimum inertia in a group of nodes"
88
89
;

90
91
92
93
94
* =============================================================================
* --- Equation Definitions ----------------------------------------------------
* =============================================================================

* --- Objective Function ------------------------------------------------------
95
96

q_obj ..
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
    + v_obj * 1000000

    =E=

    // Sum over all the samples, forecasts, and time steps in the current model
    + sum(msft(m, s, f, t),
        // Probability (weight coefficient) of (s,f,t)
        + p_sft_Probability(s,f,t)
            * [
                // Time step length dependent costs
                + p_stepLength(m, f, t)
                    * [
                        // Variable O&M costs
                        + sum(gnu_output(grid, node, unit),  // Calculated only for output energy
                            + v_gen(grid, node, unit, f, t)${nuft(node, unit, f, t)}
                                * p_unit(unit, 'omCosts')
*                                 $$ifi not '%rampSched%' == 'yes' * p_stepLength(m, f, t)
*                                 $$ifi '%rampSched%' == 'yes' * (p_stepLength(m, f, t) + p_stepLength(m, f, t+1))/2
                            ) // END sum(gnu_output)

                        // Fuel and emission costs
                        + sum((uft(unit_fuel, f, t), fuel)${uFuel(unit_fuel, 'main', fuel)},
                            + v_fuelUse(fuel, unit_fuel, f, t)
                                * [
                                    + sum(tFuel$[ord(tFuel) <= ord(t)], // Fuel costs, sum initial fuel price plus all subsequent changes to the fuelprice
                                        + ts_fuelPriceChange(fuel, tFuel)
                                        )
                                    + sum(emission, // Emission taxes
                                        + p_unitFuelEmissionCost(unit_fuel, fuel, emission)
                                        )
                                    ] // END * v_fuelUse
                            ) // END sum(uft)

                        // Node state slack variable penalties
                        + sum(gn_stateSlack(grid, node),
                            + sum(slack${p_gnBoundaryPropertiesForStates(grid, node, slack, 'slackCost')},
                                + v_stateSlack(grid, node, slack, f, t)
                                    * p_gnBoundaryPropertiesForStates(grid, node, slack, 'slackCost')
                                ) // END sum(slack)
                            ) // END sum(gn_stateSlack)

                        // Dummy variable penalties
                        // Energy balance feasibility dummy varible penalties
                        + sum(inc_dec,
                            + sum(gn(grid, node),
                                + vq_gen(inc_dec, grid, node, f, t)
                                    * PENALTY_BALANCE(grid)
                                ) // END sum(gn)
                            ) // END sum(inc_dec)

                        // Reserve provision feasibility dummy variable penalties
                        + sum(restypeDirectionNode(restype, up_down, node),
                            + vq_resDemand(restype, up_down, node, f, t)
                                * PENALTY_RES(restype, up_down)
                            ) // END sum(restypeDirectionNode)

                        ] // END * p_stepLength

                // Start-up costs
                + sum(uft_online(unit, f, t),
                    + sum(starttype,
                        + v_startup(unit, starttype, f, t) // Cost of starting up
                            * [ // Startup variable costs
                                + p_uStartup(unit, starttype, 'cost', 'unit')${not unit_investLP(unit)}
                                + p_uStartup(unit, starttype, 'cost', 'capacity')${unit_investLP(unit)}

                                // Start-up fuel and emission costs
                                + sum(uFuel(unit, 'startup', fuel)${unit_fuel(unit)},
                                    + (
                                        + p_uStartup(unit, starttype, 'consumption', 'unit')${not unit_investLP(unit)}
                                        + p_uStartup(unit, starttype, 'consumption', 'capacity')$unit_investLP(unit)
                                        )
                                        * [
                                            + sum(tFuel$[ord(tFuel) <= ord(t)], // Fuel costs for start-up fuel use
                                                + ts_fuelPriceChange(fuel, tFuel)
                                                ) // END sum(tFuel)
                                            + sum(emission, // Emission taxes of startup fuel use
                                                + p_unitFuelEmissionCost(unit, fuel, emission)
                                                ) // END sum(emission)
                                            ] // END * p_uStartup
                                        ) // END sum(uFuel)
                                ] // END * v_startup
                        ) // END sum(starttype)
                    ) // END sum(uft_online)

                // Ramping costs
                + sum(gnuft_ramp(grid, node, unit, f, t)${  [   p_gnu(grid, node, unit, 'rampUpCost')
                                                                or p_gnu(grid, node, unit, 'rampDownCost')
                                                                ]
                                                            and ord(t) > mSettings(m, 't_start')
                                                            },
                    + p_gnu(grid, node, unit, 'rampUpCost') * v_genRampChange(grid, node, unit, 'up', f, t)
                    + p_gnu(grid, node, unit, 'rampDownCost') * v_genRampChange(grid, node, unit, 'down', f, t)
                    ) // END sum(gnuft_ramp)

                ]  // END * p_sft_probability(s,f,t)
        ) // END sum over msft(m, s, f, t)

195
    // Value of energy storage change
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
    + sum(gn_state(grid, node)${active('storageValue')},
        + sum(mftStart(m, f, t)${p_storageValue(grid, node, t)},
            + v_state(grid, node, f, t)
                * p_storageValue(grid, node, t)
                * sum(s${p_sft_probability(s, f, t)},
                    + p_sft_probability(s, f, t)
                    ) // END sum(s)
            ) // END sum(mftStart)
        - sum(mftLastSteps(m, f, t)${p_storageValue(grid, node, t)},
            + v_state(grid, node, f, t)
                * p_storageValue(grid, node, t)
                * sum(s${p_sft_probability(s, f, t)},
                    + p_sft_probability(s, f, t)
                    ) // END sum(s)
            ) // END sum(mftLastSteps)
        ) // END sum(gn_state)

    // Investment Costs
    + sum(t_invest(t),
        // Unit investment costs
        + sum(gnu(grid, node, unit),
            + v_invest_LP(unit, t)
                * p_gnu(grid, node, unit, 'invCosts')
                * p_gnu(grid, node, unit, 'annuity')
            + v_invest_MIP(unit, t)
                * p_gnu(grid, node, unit, 'unitSizeTot')
                * p_gnu(grid, node, unit, 'invCosts') * p_gnu(grid, node, unit, 'annuity')
            ) // END sum(gnu)

        // Transfer link investment costs
        + sum(gn2n_directional(grid, from_node, to_node),
            + v_investTransfer_LP(grid, from_node, to_node, t)
                * [
                    + p_gnn(grid, from_node, to_node, 'invCost')
                        * p_gnn(grid, from_node, to_node, 'annuity')
                    + p_gnn(grid, to_node, from_node, 'invCost')
                        * p_gnn(grid, to_node, from_node, 'annuity')
                    ] // END * v_investTransfer_LP
            + v_investTransfer_MIP(grid, from_node, to_node, t)
                * [
                    + p_gnn(grid, from_node, to_node, 'unitSize')
                        * p_gnn(grid, from_node, to_node, 'invCost')
                        * p_gnn(grid, from_node, to_node, 'annuity')
                    + p_gnn(grid, to_node, from_node, 'unitSize')
                        * p_gnn(grid, to_node, from_node, 'invCost')
                        * p_gnn(grid, to_node, from_node, 'annuity')
                    ] // END * v_investTransfer_MIP
            ) // END sum(gn2n_directional)
        ) // END sum(t_invest)

246
247
$ontext
    // "Value" of online units, !!! TEMPORARY MEASURES !!!
248
  - sum([s, m, uft_online(unit, ft_dynamic(f,t))]$mftStart(m, f, t),
249
250
251
252
253
        + p_sft_probability(s, f, t) * 0.5
            * (
                + v_online(unit, f+cf(f,t), t) * p_unit(unit, 'startCost')
                + v_online_LP(unit, f+cf(f,t), t) * p_unit(unit, 'startCost_MW')
              )
254
        ) // minus value of avoiding startup costs before
255
  - sum((s, uft_online_last(unit, ft_dynamic(f,t))),
256
257
258
259
260
        + p_sft_probability(s, f, t) * 0.5
            * (
                + v_online(unit, f+cf(f,t), t) * p_unit(unit, 'startCost')
                + v_online_LP(unit, f+cf(f,t), t) * p_unit(unit, 'startCost_MW')
              )
261
        ) // or after the model solve
262
$offtext
263
;
264

265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
* --- Energy Balance ----------------------------------------------------------

q_balance(gn(grid, node), mft(m, f, t))${   not p_gn(grid, node, 'boundAll')
                                            } .. // Energy/power balance dynamics solved using implicit Euler discretization

    // The left side of the equation is the change in the state (will be zero if the node doesn't have a state)
    + p_gn(grid, node, 'energyStoredPerUnitOfState')${gn_state(grid, node)} // Unit conversion between v_state of a particular node and energy variables (defaults to 1, but can have node based values if e.g. v_state is in Kelvins and each node has a different heat storage capacity)
        * [
            + v_state(grid, node, f+df_central(f,t), t)                   // The difference between current
            - v_state(grid, node, f+df(f,t+dt(t)), t+dt(t))                     // ... and previous state of the node
            ]

    =E=

    // The right side of the equation contains all the changes converted to energy terms
    + p_stepLength(m, f, t) // Multiply with the length of the timestep to convert power into energy
        $$ifi '%rampSched%' == 'yes' / 2    // Averaging all the terms on the right side of the equation over the timestep here.
        * (
            // Self discharge out of the model boundaries
            - p_gn(grid, node, 'selfDischargeLoss')${gn_state(grid, node)}
                * [
                    + v_state(grid, node, f+df_Central(f,t), t) // The current state of the node
                    $$ifi '%rampSched%' == 'yes' + v_state(grid, node, f+df(f,t+dt(t)), t+dt(t)) // and possibly averaging with the previous state of the node
                    ]

            // Energy diffusion from this node to neighbouring nodes
            - sum(to_node${gnn_state(grid, node, to_node)},
                + p_gnn(grid, node, to_node, 'diffCoeff')
                    * [
                        + v_state(grid, node, f+df_Central(f,t), t)
                        $$ifi '%rampSched%' == 'yes' + v_state(grid, node, f+df(f,t+dt(t)), t+dt(t))
                        ]
                ) // END sum(to_node)

            // Energy diffusion from neighbouring nodes to this node
            + sum(from_node${gnn_state(grid, from_node, node)},
                + p_gnn(grid, from_node, node, 'diffCoeff')
                    * [
                        + v_state(grid, from_node, f+df_Central(f,t), t) // Incoming diffusion based on the state of the neighbouring node
                        $$ifi '%rampSched%' == 'yes' + v_state(grid, from_node, f+df(f,t+dt(t)), t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                ) // END sum(from_node)

            // Controlled energy transfer, applies when the current node is on the left side of the connection
            - sum(node_${gn2n_directional(grid, node, node_)},
                + (1 - p_gnn(grid, node, node_, 'transferLoss')) // Reduce transfer losses
                    * [
                        + v_transfer(grid, node, node_, f, t)
                        $$ifi '%rampSched%' == 'yes' + v_transfer(grid, node, node_, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                + p_gnn(grid, node, node_, 'transferLoss') // Add transfer losses back if transfer is from this node to another node
                    * [
                        + v_transferRightward(grid, node, node_, f, t)
                        $$ifi '%rampSched%' == 'yes' + v_transferRightward(grid, node, node_, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                ) // END sum(node_)

            // Controlled energy transfer, applies when the current node is on the right side of the connection
            + sum(node_${gn2n_directional(grid, node_, node)},
                + [
                    + v_transfer(grid, node_, node, f, t)
                    $$ifi '%rampSched%' == 'yes' + v_transfer(grid, node_, node, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                    ]
                - p_gnn(grid, node_, node, 'transferLoss') // Reduce transfer losses if transfer is from another node to this node
                    * [
                        + v_transferRightward(grid, node_, node, f, t)
                        $$ifi '%rampSched%' == 'yes' + v_transferRightward(grid, node_, node, f, t+dt(t)) // Ramp schedule averaging, NOTE! State and other terms use different indeces for non-ramp-schedule!
                        ]
                ) // END sum(node_)

            // Interactions between the node and its units
            + sum(gnuft(grid, node, unit, f, t),
                + v_gen(grid, node, unit, f, t) // Unit energy generation and consumption
                $$ifi '%rampSched%' == 'yes' + v_gen(grid, node, unit, f, t+dt(t))
339
                )
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354

            // Spilling energy out of the endogenous grids in the model
            - v_spill(grid, node, f, t)${node_spill(node)}
            $$ifi '%rampSched%' == 'yes' - v_spill(grid, node, f, t)${node_spill(node)}

            // Power inflow and outflow timeseries to/from the node
            + ts_influx_(grid, node, f, t)   // Incoming (positive) and outgoing (negative) absolute value time series
            $$ifi '%rampSched%' == 'yes' + ts_influx_(grid, node, f, t+dt(t))

            // Dummy generation variables, for feasibility purposes
            + vq_gen('increase', grid, node, f, t) // Note! When stateSlack is permitted, have to take caution with the penalties so that it will be used first
            $$ifi '%rampSched%' == 'yes' + vq_gen('increase', grid, node, f, t+dt(t))
            - vq_gen('decrease', grid, node, f, t) // Note! When stateSlack is permitted, have to take caution with the penalties so that it will be used first
            $$ifi '%rampSched%' == 'yes' - vq_gen('decrease', grid, node, f, t+dt(t))
    ) // END * p_stepLength
355
;
356
357
358

* --- Reserve Demand ----------------------------------------------------------

359
q_resDemand(restypeDirectionNode(restype, up_down, node), ft(f, t))${   ord(t) < tSolveFirst + sum[mf(m, f), mSettings(m, 't_reserveLength')]
Topi Rasku's avatar
Topi Rasku committed
360
                                                                        } ..
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
    // Reserve provision by capable units on this node
    + sum(nuft(node, unit, f, t)${nuRescapable(restype, up_down, node, unit)},
        + v_reserve(restype, up_down, node, unit, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(nuft)

    // Reserve provision to this node via transfer links
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNode(restype, up_down, node_)},
        + (1 - p_gnn(grid, node_, node, 'transferLoss') )
            * v_resTransferRightward(restype, up_down, node_, node, f+df_nReserves(node_, restype, f, t), t)             // Reserves from another node - reduces the need for reserves in the node
        ) // END sum(gn2n_directional)
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNode(restype, up_down, node_)},
        + (1 - p_gnn(grid, node, node_, 'transferLoss') )
            * v_resTransferLeftward(restype, up_down, node, node_, f+df_nReserves(node_, restype, f, t), t)             // Reserves from another node - reduces the need for reserves in the node
        ) // END sum(gn2n_directional)

    =G=

    // Demand for reserves
    + ts_reserveDemand_(restype, up_down, node, f, t)${p_nReserves(node, restype, 'use_time_series')}
    + p_nReserves(node, restype, up_down)${not p_nReserves(node, restype, 'use_time_series')}

    // Reserve provisions to another nodes via transfer links
    + sum(gn2n_directional(grid, node, node_)${restypeDirectionNode(restype, up_down, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
        + v_resTransferRightward(restype, up_down, node, node_, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(gn2n_directional)
    + sum(gn2n_directional(grid, node_, node)${restypeDirectionNode(restype, up_down, node_)},   // If trasferring reserves to another node, increase your own reserves by same amount
        + v_resTransferLeftward(restype, up_down, node_, node, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(gn2n_directional)

    // Reserve demand feasibility dummy variables
    - vq_resDemand(restype, up_down, node, f, t)

393
;
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467

* --- Maximum Downward Capacity -----------------------------------------------

q_maxDownward(m, gnuft(grid, node, unit, f, t))${   [   ord(t) < tSolveFirst + mSettings(m, 't_reserveLength') // Unit is either providing
                                                        and sum(restype, nuRescapable(restype, 'down', node, unit)) // downward reserves
                                                        ]
                                                    // NOTE!!! Could be better to form a gnuft_reserves subset?
                                                    or [ // the unit has an online variable
                                                        uft_online(unit, f, t)
                                                        and [
                                                            (unit_minLoad(unit) and p_gnu(grid, node, unit, 'unitSizeGen')) // generators with a min. load
                                                            or p_gnu(grid, node, unit, 'maxCons') // or consuming units with an online variable
                                                            ]
                                                        ] // END or
                                                    or [ // consuming units with investment possibility
                                                        gnu_input(grid, node, unit)
                                                        and [unit_investLP(unit) or unit_investMIP(unit)]
                                                        ]
                                                    } ..

    // Energy generation/consumption
    + v_gen(grid, node, unit, f, t)

    // Considering output constraints (e.g. cV line)
    + sum(gngnu_constrainedOutputRatio(grid, node, grid_, node_, unit),
        + p_gnu(grid_, node_, unit, 'cV')
            * v_gen(grid_, node_, unit, f, t)
        ) // END sum(gngnu_constrainedOutputRatio)

    // Downward reserve participation
    - sum(nuRescapable(restype, 'down', node, unit)${ord(t) < tSolveFirst + mSettings(m, 't_reserveLength')},
        + v_reserve(restype, 'down', node, unit, f+df_nReserves(node, restype, f, t), t) // (v_reserve can be used only if the unit is capable of providing a particular reserve)
        ) // END sum(nuRescapable)

    =G= // Must be greater than minimum load or maximum consumption  (units with min-load and both generation and consumption are not allowed)

    // Generation units, greater than minload
    + p_gnu(grid, node, unit, 'unitSizeGen')
        * sum(effGroup, // Uses the minimum 'lb' for the current efficiency approximation
            + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
            + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
            ) // END sum(effGroup)
        * [ // Online variables should only be generated for units with restrictions
            + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)} // LP online variant
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)} // MIP online variant
            ] // END v_online

    // Consuming units, greater than maxCons
    // Available capacity restrictions
    - p_unit(unit, 'availability')
        * [
            // Capacity factors for flow units
            + sum(flow${flowUnit(flow, unit)},
                + ts_cf_(flow, node, f, t)
                ) // END sum(flow)
            + 1${not unit_flow(unit)}
            ] // END * p_unit(availability)
        * [
            // Online capacity restriction
            + p_gnu(grid, node, unit, 'maxCons')${not uft_online(unit, f, t)} // Use initial maximum if no online variables
            + p_gnu(grid, node, unit, 'unitSizeCons')
                // Investments to additional non-online capacity
                * sum(t_invest(t_)${    ord(t_)<=ord(t)
                                        and not uft_online(unit, f, t)
                                        },
                    + v_invest_LP(unit, t_)${unit_investLP(unit)} // NOTE! v_invest_LP also for consuming units is positive
                    + v_invest_MIP(unit, t_)${unit_investMIP(unit)} // NOTE! v_invest_MIP also for consuming units is positive
                    ) // END sum(t_invest)
                // Capacity online
                * [
                    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
                    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
                    ] // END * p_gnu(unitSizeCons)
            ] // END * p_unit(availability)
468
;
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540

* --- Maximum Upwards Capacity ------------------------------------------------

q_maxUpward(m, gnuft(grid, node, unit, f, t))${ [   ord(t) < tSolveFirst + mSettings(m, 't_reserveLength') // Unit is either providing
                                                    and sum(restype, nuRescapable(restype, 'up', node, unit)) // upward reserves
                                                    ]
                                                or [
                                                    uft_online(unit, f, t) // or the unit has an online variable
                                                        and [
                                                            [unit_minLoad(unit) and p_gnu(grid, node, unit, 'unitSizeCons')] // consuming units with min_load
                                                            or [p_gnu(grid, node, unit, 'maxGen')]                          // generators with an online variable
                                                            ]
                                                    ]
                                                or [
                                                    gnu_output(grid, node, unit) // generators with investment possibility
                                                    and (unit_investLP(unit) or unit_investMIP(unit))
                                                    ]
                                                }..
    // Energy generation/consumption
    + v_gen(grid, node, unit, f, t)

    // Considering output constraints (e.g. cV line)
    + sum(gngnu_constrainedOutputRatio(grid, node, grid_output, node_, unit),
        + p_gnu(grid_output, node_, unit, 'cV')
            * v_gen(grid_output, node_, unit, f, t)
        ) // END sum(gngnu_constrainedOutputRatio)

    // Upwards reserve participation
    + sum(nuRescapable(restype, 'up', node, unit)${ord(t) < tSolveFirst + mSettings(m, 't_reserveLength')},
        + v_reserve(restype, 'up', node, unit, f+df_nReserves(node, restype, f, t), t)
        ) // END sum(nuRescapable)

    =L= // must be less than available/online capacity

    // Consuming units
    + p_gnu(grid, node, unit, 'unitSizeCons')
        * sum(effGroup, // Uses the minimum 'lb' for the current efficiency approximation
            + p_effGroupUnit(effGroup, unit, 'lb')${not ts_effGroupUnit(effGroup, unit, 'lb', f, t)}
            + ts_effGroupUnit(effGroup, unit, 'lb', f, t)
            ) // END sum(effGroup)
        * [
            + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)} // Consuming units are restricted by their min. load (consuming is negative)
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)} // Consuming units are restricted by their min. load (consuming is negative)
            ] // END * p_gnu(unitSizeCons)

    // Generation units
    // Available capacity restrictions
    + p_unit(unit, 'availability') // Generation units are restricted by their (available) capacity
        * [
            // Capacity factor for flow units
            + sum(flow${flowUnit(flow, unit)},
                + ts_cf_(flow, node, f, t)
                ) // END sum(flow)
            + 1${not unit_flow(unit)}
            ] // END * p_unit(availability)
        * [
            // Online capacity restriction
            + p_gnu(grid, node, unit, 'maxGen')${not uft_online(unit, f, t)} // Use initial maxGen if no online variables
            + p_gnu(grid, node, unit, 'unitSizeGen')
                // Investments to non-online capacity
                * sum(t_invest(t_)${    ord(t_)<=ord(t)
                                        and not uft_online(unit, f ,t)
                                        },
                    + v_invest_LP(unit, t_)${unit_investLP(unit)}
                    + v_invest_MIP(unit, t_)${unit_investMIP(unit)}
                    ) // END sum(t_invest)
                // Capacity online
                * [
                    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f ,t)}
                    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
                    ] // END * p_gnu(unitSizeGen)
            ] // END * p_unit(availability)
541
;
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561

* --- Unit Startup and Shutdown -----------------------------------------------

q_startup(uft_online(unit, f, t)) ..

    // Units currently online
    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}

    =E=

    // Units previously online
    + v_online_LP(unit, f+df(f,t+dt(t)), t+dt(t))${uft_onlineLP(unit, f, t+dt(t))} // This reaches to tFirstSolve when pt = -1
    + v_online_MIP(unit, f+df(f,t+dt(t)), t+dt(t))${uft_onlineMIP(unit, f, t+dt(t))}

    // Unit startup and shutdown
    + sum(starttype,
        + v_startup(unit, starttype, f, t)
        ) // END sum(starttype)
    - v_shutdown(unit, f, t)
562
;
563

564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
*--- Startup Type -------------------------------------------------------------

q_startuptype(m, starttypeConstrained(starttype), uft_online(unit, f, t)) ..

    // Startup type
    + v_startup(unit, starttype, f, t)

    =L=

    // Subunit shutdowns within special startup timeframe
    + sum(t_${  ord(t_) > [ord(t)-p_uNonoperational(unit, starttype, 'max') / mSettings(m, 'intervalInHours') / p_stepLengthNoReset(m, f, t_)]
                and ord(t_)<=[ord(t)-p_uNonoperational(unit, starttype, 'min') / mSettings(m, 'intervalInHours') / p_stepLengthNoReset(m, f, t_)]
                and p_stepLengthNoReset(m, f, t_)
        },
          + v_shutdown(unit, f+df(f,t_), t_)
    ) // END sum(t_)
;

*--- Online Limits with Startup Type Constraints and Investments --------------

q_onlineLimit(m, uft_online(unit, f, t))${  p_unit(unit, 'minShutDownTime')
                                            or unit_investLP(unit)
                                            or unit_investMIP(unit)
                                            } ..
    // Online variables
    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f ,t)}

    =L=

    // Number of existing units
    + p_unit(unit, 'unitCount')

    // Number of units unable to start due to restrictions
    - sum(t_${  ord(t_)>=[ord(t)-p_unit(unit, 'minShutDownTime') / mSettings(m, 'intervalInHours')]
                and ord(t_)<ord(t)
                and p_stepLengthNoReset(m, f+df(f,t_), t_)
                },
        + v_shutdown(unit, f+df(f,t_), t_)
    ) // END sum(t_)

    // Investments into units
    + sum(t_invest(t_)${ord(t_)<=ord(t)},
        + v_invest_LP(unit, t_)
        + v_invest_MIP(unit, t_)
        ) // END sum(t_invest)
;

*--- Minimum Unit Uptime ------------------------------------------------------

q_onlineMinUptime(m, uft_online(unit, f, t))${  p_unit(unit, 'minOperationTime')
                                                } ..

    // Units currently online
    + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}

    =G=

    // Units that have minimum operation time requirements active
    + sum(t_${  ord(t_)>=[ord(t)-p_unit(unit, 'minOperationTime') / mSettings(m, 'intervalInHours') / p_stepLengthNoReset(m,f,t_)]
                and ord(t_)<ord(t)
                and p_stepLengthNoReset(m, f, t_)
                },
        + sum(starttype,
            + v_startup(unit, starttype, f+df(f,t_), t_)
            ) // END sum(starttype)
    ) // END sum(t_)
;

634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
* --- Ramp Constraints --------------------------------------------------------
// !!! CURRENTLY REMOVED, PENDING CHANGE !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
$ontext
q_genRamp(gn(grid, node), m, s, uft(unit, f, t))${  gnuft_ramp(grid, node, unit, f, t)
                                                    and ord(t) > msStart(m, s)
                                                    and ord(t) <= msEnd(m, s)
                                                    } ..

    + sum(ramp, // Sum over the ramp categories
        + v_genRamp(ramp, grid, node, unit, f, t)
            * p_stepLength(m, f, t)
        ) // END sum(ramp)

    =E=

    // Change in generation over the time step
    + v_gen(grid, node, unit, f, t)
    - v_gen(grid, node, unit, f+df(f,t), t+dt(t))
652
;
653
$offtext
654
* -----------------------------------------------------------------------------
655
$ontext
Niina Helistö's avatar
Niina Helistö committed
656
657
658
659
q_genRampChange(gn(grid, node), m, s, unit, ft(f, t))${ gnuft_ramp(grid, node, unit, f, t)
*                                                     and ord(t) > mSettings(m, 't_start')
                                                     and ord(t) > msStart(m, s)
                                                     and ord(t) <= msEnd(m, s)
660
661
662
663
                                                     and [ p_gnu(grid, node, unit, 'rampUpCost')
                                                           or p_gnu(grid, node, unit, 'rampDownCost')
                                                           ]
                                                     } ..
664
665
    + v_genRampChange(grid, node, unit, 'up', f+pf(f,t), t+pt(t))
    - v_genRampChange(grid, node, unit, 'down', f+pf(f,t), t+pt(t))
666
    =E=
667
    + v_genRamp(grid, node, unit, f, t)
668
    - v_genRamp(grid, node, unit, f+pf(f,t), t+pt(t));
669
670
$offtext

671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
* --- Ramp Up Limits ----------------------------------------------------------
// !!! PENDING CHANGES !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// The way ramp limits are defined are waiting changes, so these equations have
// to be rewritten in the future.
$ontext
q_rampUpLimit(gn(grid, node), m, s, unit, ft(f, t))${ gnuft_ramp(grid, node, unit, f, t)
                                                   and ord(t) > msStart(m, s)
                                                   and msft(m, s, f, t)
                                                   and p_gnu(grid, node, unit, 'maxRampUp')
                                                   and (uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))
                                                           or unit_investLP(unit)
                                                           or unit_investMIP(unit))
                                                   } ..
  + v_genRamp(grid, node, unit, f, t+pt(t))
  =L=
    // Ramping capability of units without online variable
  + (
      + ( p_gnu(grid, node, unit, 'maxGen') - p_gnu(grid, node, unit, 'maxCons') )${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + sum(t_$(ord(t_)<=ord(t)),
          + v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxGenCap')}
          - v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxConsCap')}
          + v_invest_MIP(unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
              * p_gnu(grid, node, unit, 'unitSizeGenNet')
        )
    )
      * p_gnu(grid, node, unit, 'maxRampUp')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
    // Ramping capability of units that were online both in the previous time step and the current time step
  + (
      + v_online_LP(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + v_online(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      - v_shutdown(unit, f+cf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
    )
      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${  not unit_investLP(unit)
                 or not p_gnu(grid, node, unit, 'unitSizeGenNet')
              }
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * p_gnu(grid, node, unit, 'maxRampUp')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
  // Newly started units are assumed to start to their minload and
  // newly shutdown units are assumed to be shut down from their minload.
  + (
      + sum(starttype, v_startup(unit, starttype, f+cf(f,t), t+pt(t)))
      - v_shutdown(unit, f+cf(f,t), t+pt(t))
    )${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${not unit_investLP(unit) or not p_gnu(grid, node, unit, 'unitSizeGenNet')}
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * sum(suft(effGroup, unit, f+cf(f,t), t), p_effGroupUnit(effGroup, unit, 'lb'))
// Reserve provision?
// Note: This constraint does not limit ramping properly for example if online subunits are
// producing at full capacity (= not possible to ramp up) and more subunits are started up.
// Take this into account in q_maxUpward or in another equation?:
// v_gen =L= (v_online(t-1) - v_shutdown(t-1)) * unitSize + v_startup(t-1) * unitSize * minLoad
;

* --- Ramp Down Limits --------------------------------------------------------
q_rampDownLimit(gn(grid, node), m, s, unit, ft(f, t))${ gnuft_ramp(grid, node, unit, f, t)
                                                     and ord(t) > msStart(m, s)
                                                     and msft(m, s, f, t)
                                                     and p_gnu(grid, node, unit, 'maxRampDown')
                                                     and (uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))
                                                             or unit_investLP(unit)
                                                             or unit_investMIP(unit))
                                                     } ..
  + v_genRamp(grid, node, unit, f, t+pt(t))
  =G=
    // Ramping capability of units without online variable
  - (
      + ( p_gnu(grid, node, unit, 'maxGen') - p_gnu(grid, node, unit, 'maxCons') )${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + sum(t_$(ord(t_)<=ord(t)),
          + v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxGenCap')}
          - v_invest_LP(grid, node, unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t)) and p_gnu(grid, node, unit, 'maxConsCap')}
          + v_invest_MIP(unit, t_)${not uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
              * p_gnu(grid, node, unit, 'unitSizeGenNet')
        )
    )
      * p_gnu(grid, node, unit, 'maxRampDown')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
    // Ramping capability of units that were online both in the previous time step and the current time step
  - (
      + v_online_LP(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      + v_online(unit, f+cpf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      - v_shutdown(unit, f+cf(f,t), t+pt(t))${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
    )
      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${  not unit_investLP(unit)
                 or not p_gnu(grid, node, unit, 'unitSizeGenNet')
              }
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * p_gnu(grid, node, unit, 'maxRampDown')
      * 60 / 100  // Unit conversion from [p.u./min] to [MW/h]
  // Newly started units are assumed to start to their minload and
  // newly shutdown units are assumed to be shut down from their minload.
  + (
      + sum(starttype, v_startup(unit, starttype, f+cf(f,t), t+pt(t)))
      - v_shutdown(unit, f+cf(f,t), t+pt(t))
    )${uft_online_incl_previous(unit, f+cpf(f,t), t+pt(t))}
      * p_gnu(grid, node, unit, 'unitSizeGenNet')
      / {
          + 1${not unit_investLP(unit) or not p_gnu(grid, node, unit, 'unitSizeGenNet')}
          + sum(gnu(grid_, node_, unit)${ unit_investLP(unit)
                                          and p_gnu(grid, node, unit, 'unitSizeGenNet')
                }, p_gnu(grid_, node_, unit, 'unitSizeTot')
            )
        } // Scaling factor to calculate online capacity in gn(grid, node) in the case of continuous investments
      * sum(suft(effGroup, unit, f+cf(f,t), t), p_effGroupUnit(effGroup, unit, 'lb'))
// Reserve provision?
;
$offtext

* --- Fixed Output Ratio ------------------------------------------------------

q_outputRatioFixed(gngnu_fixedOutputRatio(grid, node, grid_, node_, unit), ft(f, t))${  uft(unit, f, t)
                                                                                        } ..

    // Generation in grid
    + v_gen(grid, node, unit, f, t)
        / p_gnu(grid, node, unit, 'cB')

    =E=

    // Generation in grid_
    + v_gen(grid_, node_, unit, f, t)
        / p_gnu(grid_, node_, unit, 'cB')
;

* --- Constrained Output Ratio ------------------------------------------------

q_outputRatioConstrained(gngnu_constrainedOutputRatio(grid, node, grid_, node_, unit), ft(f, t))${  uft(unit, f, t)
                                                                                                    } ..

    // Generation in grid
    + v_gen(grid, node, unit, f, t)
        / p_gnu(grid, node, unit, 'cB')

    =G=

    // Generation in grid_
    + v_gen(grid_, node_, unit, f, t)
        / p_gnu(grid_, node_, unit, 'cB')
;

* --- Direct Input-Output Conversion ------------------------------------------

q_conversionDirectInputOutput(suft(effDirect, unit, f, t)) ..

    // Sum over endogenous energy inputs
    - sum(gnu_input(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
        ) // END sum(gnu_input)

    // Sum over fuel energy inputs
    + sum(uFuel(unit, 'main', fuel),
        + v_fuelUse(fuel, unit, f, t)
        ) // END sum(uFuel)

    =E=

    // Sum over energy outputs
    + sum(gnu_output(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
            * [ // Heat rate
                + p_effUnit(effDirect, unit, effDirect, 'slope')${not ts_effUnit(effDirect, unit, effDirect, 'slope', f, t)}
                + ts_effUnit(effDirect, unit, effDirect, 'slope', f, t)
                ] // END * v_gen
        ) // END sum(gnu_output)

    // Consumption of keeping units online
    + sum(gnu_output(grid, node, unit),
        + p_gnu(grid, node, unit, 'unitSizeGen')
        ) // END sum(gnu_output)
        * [
            + v_online_LP(unit, f, t)${uft_onlineLP(unit, f, t)}
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
            ] // END * sum(gnu_output)
        * [
            + p_effGroupUnit(effDirect, unit, 'section')${not ts_effUnit(effDirect, unit, effDirect, 'section', f, t)}
            + ts_effUnit(effDirect, unit, effDirect, 'section', f, t)
            ] // END * sum(gnu_output)
;

* --- SOS2 Efficiency Approximation -------------------------------------------

871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
q_conversionSOS2InputIntermediate(suft(effLambda(effGroup), unit, f, t)) ..

    // Sum over endogenous energy inputs
    - sum(gnu_input(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
        ) // END sum(gnu_input)

    // Sum over fuel energy inputs
    + sum(uFuel(unit, 'main', fuel),
        + v_fuelUse(fuel, unit, f, t)
        ) // END sum(uFuel)

    =E=

    // Sum over the endogenous outputs of the unit
    + sum(gnu_output(grid, node, unit), p_gnu(grid, node, unit, 'unitSizeGen'))
        * [
            // Consumption of generation
            + sum(effSelector${effGroupSelectorUnit(effGroup, unit, effSelector)},
                + v_sos2(unit, f, t, effSelector)
                    * [ // Operation points convert the v_sos2 variables into share of capacity used for generation
                        + p_effUnit(effGroup, unit, effSelector, 'op')${not ts_effUnit(effGroup, unit, effSelector, 'op', f, t)}
                        + ts_effUnit(effGroup, unit, effSelector, 'op', f, t)
                        ] // END * v_sos2
                    * [ // Heat rate
                        + p_effUnit(effGroup, unit, effSelector, 'slope')${not ts_effUnit(effGroup, unit, effSelector, 'slope', f, t)}
                        + ts_effUnit(effGroup, unit, effSelector, 'slope', f, t)
                        ] // END * v_sos2
                ) // END sum(effSelector)

            // Consumption of keeping units online
            + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
                * p_effGroupUnit(effGroup, unit, 'section')
            ] // END * sum(gnu_output)
905
;
906
907
908
909
910
911
912
913
914
915
916
917
918
919

* --- SOS 2 Efficiency Approximation Online Variables -------------------------

q_conversionSOS2Constraint(suft(effLambda(effGroup), unit, f, t)) ..

    // Total value of the v_sos2 equals the number of online units
    + sum(effSelector${effGroupSelectorUnit(effGroup, unit, effSelector)},
        + v_sos2(unit, f, t, effSelector)
        ) // END sum(effSelector)

    =E=

    // Number of units online
    + v_online_MIP(unit, f, t)${uft_onlineMIP(unit, f, t)}
920
;
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943

* --- SOS 2 Efficiency Approximation Output Generation ------------------------

q_conversionSOS2IntermediateOutput(suft(effLambda(effGroup), unit, f, t)) ..

    // Endogenous energy output
    + sum(gnu_output(grid, node, unit),
        + p_gnu(grid, node, unit, 'unitSizeGen')
        ) // END sum(gnu_output)
        * sum(effSelector${effGroupSelectorUnit(effGroup, unit, effSelector)},
            + v_sos2(unit, f, t, effSelector)
            * [ // Operation points convert v_sos2 into share of capacity used for generation
                + p_effUnit(effGroup, unit, effSelector, 'op')${not ts_effUnit(effGroup, unit, effSelector, 'op', f, t)}
                + ts_effUnit(effGroup, unit, effSelector, 'op', f, t)
                ] // END * v_sos2
            ) // END sum(effSelector)

    =E=

    // Energy output into v_gen
    + sum(gnu_output(grid, node, unit),
        + v_gen(grid, node, unit, f, t)
        ) // END sum(gnu_output)
Juha Kiviluoma's avatar
Juha Kiviluoma committed
944
;
945

946
947
948
949
950
*--- Fixed Investment Ratios --------------------------------------------------
// !!! PENDING FIX !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// v_invest(unit) instead of the old v_invest(grid, node, unit)
// Are these even necessary anymore, if investment is unitwise?
// Maybe for batteries etc?
951

952
953
q_fixedGenCap1U(gnu(grid, node, unit), t_invest(t))${   unit_investLP(unit)
                                                        } ..
954

955
956
    // Investment
    + v_invest_LP(unit, t)
957
958
959

    =E=

960
961
962
963
964
965
966
967
    // Capacity Ratios?
    + sum(gn(grid_, node_),
        + v_invest_LP(unit, t)
        ) // END sum(gn)
        * p_gnu(grid, node, unit, 'unitSizeTot')
        / sum(gn(grid_, node_),
            + p_gnu(grid_, node_, unit, 'unitSizeTot')
            ) // END sum(gn)
968
;
969

970
971
972
*--- Fixed Investment Ratios 2 ------------------------------------------------
// !!! PENDING FIX !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// See notes in the above equation
973

974
975
q_fixedGenCap2U(grid, node, unit, grid_, node_, unit_, t_invest(t))${   p_gnugnu(grid, node, unit, grid_, node_, unit_, 'capacityRatio')
                                                                        } ..
976

977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
    // Investment
    + v_invest_LP(unit, t)
    + v_invest_MIP(unit, t)

    =E=

    // Capacity Ratio?
    + p_gnugnu(grid, node, unit, grid_, node_, unit_, 'capacityRatio')
        * [
            + v_invest_LP(unit_, t)
            + v_invest_MIP(unit_, t)
            ] // END * p_gngnu(capacityRatio)
;

* --- Total Transfer Limits ---------------------------------------------------

q_transfer(gn2n_directional(grid, node, node_), ft(f, t)) ..

    // Rightward + Leftward
    + v_transferRightward(grid, node, node_, f, t)
    - v_transferLeftward(grid, node, node_, f, t)

    =E=